# Highest Common Factor of 306, 855, 54, 945 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 306, 855, 54, 945 i.e. 9 the largest integer that leaves a remainder zero for all numbers.

HCF of 306, 855, 54, 945 is 9 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 306, 855, 54, 945 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 306, 855, 54, 945 is 9.

HCF(306, 855, 54, 945) = 9

## HCF of 306, 855, 54, 945 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 306, 855, 54, 945 is 9. ### Highest Common Factor of 306,855,54,945 is 9

Step 1: Since 855 > 306, we apply the division lemma to 855 and 306, to get

855 = 306 x 2 + 243

Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 243 and 306, to get

306 = 243 x 1 + 63

Step 3: We consider the new divisor 243 and the new remainder 63, and apply the division lemma to get

243 = 63 x 3 + 54

We consider the new divisor 63 and the new remainder 54,and apply the division lemma to get

63 = 54 x 1 + 9

We consider the new divisor 54 and the new remainder 9,and apply the division lemma to get

54 = 9 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 306 and 855 is 9

Notice that 9 = HCF(54,9) = HCF(63,54) = HCF(243,63) = HCF(306,243) = HCF(855,306) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 54 > 9, we apply the division lemma to 54 and 9, to get

54 = 9 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 54 is 9

Notice that 9 = HCF(54,9) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 945 > 9, we apply the division lemma to 945 and 9, to get

945 = 9 x 105 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 945 is 9

Notice that 9 = HCF(945,9) .

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### Frequently Asked Questions on HCF of 306, 855, 54, 945 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 306, 855, 54, 945?

Answer: HCF of 306, 855, 54, 945 is 9 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 306, 855, 54, 945 using Euclid's Algorithm?

Answer: For arbitrary numbers 306, 855, 54, 945 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.